Details

Time bar (total: 19.4s)

sample97.0ms

Algorithm
intervals
Results
21.0ms43×body2560valid
21.0ms164×body80valid
14.0ms32×body1280valid
6.0ms80×body80nan
5.0ms16×body640valid
5.0ms8×body5120valid
2.0ms7×body320valid
1.0ms6×body160valid

simplify96.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
014365
125365
246325
386325
4119325
5128325
done128325

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
0.2b
(* (* 4.0 a) c)
1.5b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
41×*-un-lft-identity
31×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
11×add-cbrt-cube add-exp-log
10×pow1 difference-of-squares
6×fma-neg associate-/l* add-log-exp
5×distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×associate-/r* flip3-- associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
2×sqrt-div associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp associate-*l* *-commutative div-inv
Counts
4 → 122
Calls
4 calls:
85.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
14.0ms
(* (* 4.0 a) c)
55.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
27.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series379.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
26.0ms
(* (* 4.0 a) c)
122.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
94.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.3s

Counts
134 → 134
Iterations

Useful iterations: done (3.3s)

IterNodesCost
021050462
153846226
2243442317
done500242267

prune840.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.3b

localize64.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt c)
0.6b
(cbrt c)
1.5b
(- (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
21.2b
(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×*-un-lft-identity
21×add-cube-cbrt
18×prod-diff
16×sqrt-prod
6×cbrt-prod fma-neg add-log-exp
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
2×flip3-- pow1/3 sqrt-div flip-- difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 84
Calls
4 calls:
1.0ms
(cbrt c)
1.0ms
(cbrt c)
68.0ms
(- (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
10.0ms
(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series965.0ms

Counts
4 → 12
Calls
4 calls:
260.0ms
(cbrt c)
331.0ms
(cbrt c)
210.0ms
(- (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
163.0ms
(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify1.6s

Counts
96 → 96
Iterations

Useful iterations: done (1.6s)

IterNodesCost
013840060
134236062
2144723290
done500023250

prune600.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 10.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt 2.0)) (sqrt 2.0))
0.4b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt 2.0))
1.5b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite253.0ms

Algorithm
rewrite-expression-head
Rules
528×times-frac
456×add-sqr-sqrt
355×*-un-lft-identity
335×sqrt-prod
255×add-cube-cbrt
100×difference-of-squares
50×distribute-lft-out--
46×associate-/l*
18×prod-diff
12×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv
6×fma-neg add-log-exp
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u
3×flip3-- div-sub flip-- associate-/l/
2×clear-num frac-2neg sqrt-div
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 427
Calls
4 calls:
79.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt 2.0)) (sqrt 2.0))
93.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt 2.0))
47.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series739.0ms

Counts
4 → 12
Calls
4 calls:
317.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt 2.0)) (sqrt 2.0))
201.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt 2.0))
112.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
439 → 439
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0441316100
11132293955
done5000286015

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt (sqrt 2.0)))
1.0b
(/ 1 (sqrt (sqrt 2.0)))
1.5b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
125×sqrt-prod
117×add-sqr-sqrt
94×*-un-lft-identity
81×times-frac
72×add-cube-cbrt
22×difference-of-squares
18×associate-/r* prod-diff
11×distribute-lft-out--
10×add-exp-log
9×associate-/l*
8×pow1 add-cbrt-cube
6×fma-neg add-log-exp
5×sqrt-pow1 pow-flip
4×expm1-log1p-u log1p-expm1-u
3×flip3-- pow1/2 div-exp flip--
2×cbrt-undiv clear-num frac-2neg sqrt-div div-inv associate-/l/
1×rem-sqrt-square rec-exp sub-neg diff-log 1-exp div-sub inv-pow
Counts
4 → 205
Calls
4 calls:
124.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt (sqrt 2.0)))
7.0ms
(/ 1 (sqrt (sqrt 2.0)))
52.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series606.0ms

Counts
4 → 10
Calls
4 calls:
401.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (sqrt (sqrt 2.0)))
0.0ms
(/ 1 (sqrt (sqrt 2.0)))
107.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
98.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
215 → 215
Iterations

Useful iterations: 2 (735.0ms)

IterNodesCost
0281101807
165591252
2279287612
done500187612

prune739.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 9.9b

regimes354.0ms

Accuracy

86.7% (3.2b remaining)

Error of 13.8b against oracle of 10.7b and baseline of 34.4b

bsearch94.0ms

Steps
ItersRangePoint
4
1.2765290296533779e-46
2.1214586855945932e-46
1.627160326743934e-46
7
-5.856362438573669e+138
-1.280729871585891e+137
-3.7108875578650606e+138

simplify13.0ms

Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0341070
1421070
done421070

end0.0ms

sample2.5s

Algorithm
intervals
Results
438.0ms1094×body2560valid
397.0ms467×body640valid
390.0ms5792×body80valid
376.0ms887×body1280valid
359.0ms243×body320valid
138.0ms2874×body80nan
100.0ms108×body5120valid
13.0ms117×body160valid